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Resolución de integrales/ sqrtx/ 6*x^5/ x*sqrt/ 2*sqrtx*sqrt(1+(16*x^5)/9)

Integral de 2*sqrtx*sqrt(1+(16*x^5)/9) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                            
  /                            
 |                             
 |               ___________   
 |              /         5    
 |      ___    /      16*x     
 |  2*\/ x *  /   1 + -----  dx
 |          \/          9      
 |                             
/                              
0
∫012x16x59+1 dx\int\limits_{0}^{1} 2 \sqrt{x} \sqrt{\frac{16 x^{5}}{9} + 1}\, dx 
Integral((2*sqrt(x))*sqrt(1 + (16*x^5)/9), (x, 0, 1))
Respuesta (Indefinida) [src] 
                                                                                       
  /                                                       _  /-1/2, 3/10 |     5  pi*I\
 |                                      3/2              |_  |           | 16*x *e    |
 |              ___________          2*x   *Gamma(3/10)* |   |    13     | -----------|
 |             /         5                              2  1 |    --     |      9     |
 |     ___    /      16*x                                    \    10     |            /
 | 2*\/ x *  /   1 + -----  dx = C + --------------------------------------------------
 |         \/          9                                       /13\                    
 |                                                      5*Gamma|--|                    
/                                                              \10/
∫2x16x59+1 dx=C+2x32Γ(310)2F1(−12,3101310|16x5eiπ9)5Γ(1310)\int 2 \sqrt{x} \sqrt{\frac{16 x^{5}}{9} + 1}\, dx = C + \frac{2 x^{\frac{3}{2}} \Gamma\left(\frac{3}{10}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{10} \\ \frac{13}{10} \end{matrix}\middle| {\frac{16 x^{5} e^{i \pi}}{9}} \right)}}{5 \Gamma\left(\frac{13}{10}\right)}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.9005
Trazar el gráfico f(x)
Respuesta [src] 
                                          
                _  /-1/2, 3/10 |     pi*I\
               |_  |           | 16*e    |
2*Gamma(3/10)* |   |    13     | --------|
              2  1 |    --     |    9    |
                   \    10     |         /
------------------------------------------
                      /13\                
               5*Gamma|--|                
                      \10/
2Γ(310)2F1(−12,3101310|16eiπ9)5Γ(1310)\frac{2 \Gamma\left(\frac{3}{10}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{10} \\ \frac{13}{10} \end{matrix}\middle| {\frac{16 e^{i \pi}}{9}} \right)}}{5 \Gamma\left(\frac{13}{10}\right)} 
=
= 
                                          
                _  /-1/2, 3/10 |     pi*I\
               |_  |           | 16*e    |
2*Gamma(3/10)* |   |    13     | --------|
              2  1 |    --     |    9    |
                   \    10     |         /
------------------------------------------
                      /13\                
               5*Gamma|--|                
                      \10/
2Γ(310)2F1(−12,3101310|16eiπ9)5Γ(1310)\frac{2 \Gamma\left(\frac{3}{10}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{10} \\ \frac{13}{10} \end{matrix}\middle| {\frac{16 e^{i \pi}}{9}} \right)}}{5 \Gamma\left(\frac{13}{10}\right)} 
2*gamma(3/10)*hyper((-1/2, 3/10), (13/10,), 16*exp_polar(pi*i)/9)/(5*gamma(13/10))
Respuesta numérica [src] 
1.56207483385934
1.56207483385934

    Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.

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